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A224070

Sets of four primes such that the sum of any three is prime, ordered first by sum, then lexicographically.

5, 7, 17, 19, 7, 11, 13, 23, 7, 13, 17, 23, 5, 13, 19, 29, 5, 11, 13, 43, 11, 13, 19, 29, 5, 7, 19, 47, 5, 17, 19, 37, 7, 11, 19, 41, 11, 17, 19, 31, 5, 11, 31, 37, 5, 13, 23, 43, 11, 13, 17, 43, 11, 13, 23, 37, 13, 17, 23, 31, 7, 11, 19, 53, 7, 11, 29, 43

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OFFSET

1,1

LINKS

T. D. Noe, Table of n, a(n) for n = 1..4000

Chris Caldwell and G. L. Honaker, Jr., Prime Curios!

EXAMPLE

The first four terms of the sequence are 5, 7, 17, 19. The sum of any three is prime: 5 + 7 + 17 = 29, 5 + 7 + 19 = 31, 5 + 17 + 19 = 41, 7 + 17 + 19 = 43. This set of four primes has the smallest possible sum, 48, and is unique.

There are two such sets of four primes with sum 72: {5, 11, 13, 43} and {11, 13, 19, 29}. The first set is listed first since it is lexicographically earliest.

MATHEMATICA

MaxSum = 100; nn = PrimePi[MaxSum - 15]; ps = {}; Do[p = Prime[{a, b, c, d}]; If[Total[p] <= MaxSum, AppendTo[ps, p]], {a, 2, nn - 3}, {b, a + 1, nn - 2}, {c, b + 1, nn - 1}, {d, c + 1, nn}]; s = Select[ps, And @@ PrimeQ /@ (Total[#] - #) &]; s2 = SortBy[s, Total]; Flatten[s2] (* T. D. Noe, Apr 01 2013 *)

CROSSREFS

Cf. A000040.

Sequence in context: A341038 A070372 A082818 * A075089 A075305 A140564

Adjacent sequences: A224067 A224068 A224069 * A224071 A224072 A224073

KEYWORD

nonn

AUTHOR

G. L. Honaker, Jr., Mar 30 2013

STATUS

approved